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Research Article | Open Access

On the linearized system of elasticity in the half-space

Department of Mathematics and Statistics, College of Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), PO-Box 90950, Riyadh 11623, KSA
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Abstract

The purpose of this paper is twofold. The first goal is to provide a simple and constructive proof of Korn inequalities in half-space with weighted norms. The proof leads to explicit values of the constants. The second objective is to use these inequalities to show that the linear elasticity system in half-space admits a coercive variational formulation. This formulation corresponds to the physical case in which the solution is evanescent at infinity.

Keywords

linear elasticity, unbounded domainsKorn's inequalityhalf-spaceweighted spaces
CLC number: 35E20, 35Q30, 76D07

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AIMS Mathematics
Volume 7 Issue 8,
August 2022
Pages 14991-15001
DOI: 10.3934/math.2022821

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Kerdid N. On the linearized system of elasticity in the half-space. AIMS Mathematics, 2022, 7(8): 14991-15001. https://doi.org/10.3934/math.2022821

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Received: 19 March 2022
Revised: 30 May 2022
Accepted: 06 June 2022
Published: 15 August 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)